Notation:

U = Turn "Up" (top) face clockwise 90º.

D = Turn "Down" (bottom) face clockwise 90º.

L = Turn Left face clockwise 90º.

R = Turn Right face clockwise 90º.

F = Turn Front face clockwise 90º.

B = Turn Back face clockwise 90º.

An apostrophe indicates the inverse of the face turn that proceeds it.

• For example, F' means that you turn the front face 90º counter-clockwise.

A face turn followed by a "2" indicates a 180º turn.

• F2 is a 180º turn of the front face.

"Clockwise" and "counter-clockwise" are always defined as though you are looking directly at that face.

When making a reference to a specific piece of the cube, I will just use the letters of the faces it touches.

• Two letters for edge pieces (i.e. UF for the edge piece of the Up and Front faces)
• Three letters for corner pieces (i.e. BDR for the Back, Down, Right corner)

Also, in examples I will sometimes use the first letters of colors to refer to specific pieces.

• RBY would refer to the Red - Blue - Yellow corner.